While it doesn't happen often, mass mortality and morbidity events have been observed in seal populations over the years due to mostly avian influenza viruses. (note: Human H1N1pdm09 was detected in Elephant Seals in 2010).

During the winter of 1979-1980 seals were found suffering from pneumonia on the Cape Cod. In that instance, the culprit turned out to be an H7N7 influenza. (see Isolation of an influenza A virus from seals G. Lang, A. Gagnon and J. R. Geraci)

Until it landed in seals, this H3N8 strain was an avian adapted virus.
That is, that it bound preferentially to the kind of receptor cells
commonly found in the digestive and respiratory tracts of birds; alpha 2,3 receptor cells.

In 2012, in mBio: A Mammalian Adapted H3N8 In Seals, we saw evidence that that particular avian virus had recently adapted to better bind to alpha 2,6 receptor cells;
the type that line the surfaces of the human upper respiratory system.

Fast forward to today, and we have a new report, published thispast week in Nature's Science Reports, that takes a deeper look at the ability of this seal H3N8 virus to bind to the mammalian alpha 2,6 receptor cell.

The authors outline their reasons for concern in the introduction:

The wide variety of IAV strains infecting seals provides opportunities
for genetic reassortment and/or adaptation, and it has been proposed
that seals might play a similar role to pigs as mixing vessels for avian
and human viruses.
With the exponential increase in protected seal populations and
urbanization of coastal cities, the seal-human interface is continuously
expanding, which creates a suitable environment for viral zoonotic
transmissions

In contrast to some of the earlier studies on this seal H3N8 virus, these researchers (using a recombinant seal H3N8 virus) found the virus still binds preferentially to avian alpha 2,3 receptor cells. The authors write:

We compared the binding patterns of recombinant HA proteins derived from
seal H3N8 against that of a seasonal human H3N2 virus
(A/Wyoming/03/2003) to fixed human lung and tracheal tissue sections. HA
proteins were allowed to bind to respiratory tissues, bound HA was
detected by immuno-staining and the results were verified against
negative control mock-stained tissue sections.

Not quite as worrisome as earlier reports suggested, but not without some concerns. The authors write:

In conclusion, seal H3N8 virus still maintains the avian-type receptor
specificity, binds to human lung tissues and replicates in human lung
carcinoma cells, which raises concerns about its potential to establish
infection in the lower respiratory tract of humans. However, we believe
that certain additional mutations will be required for this virus to
gain human transmissibility.

Follow the link below for the full study, which includes a great deal of technical detail on how they created a recombinant HA for testing.